Chapter 1
The Benefits
and Risks of
Using Statistics
Copyright ©2005 Brooks/Cole, a division of Thomson Learning, Inc.
Thought Question 1:
A recent newspaper article concluded that
smoking marijuana at least three times a
week resulted in lower grades
in college.
How do you think the researchers came
to this conclusion? Do you believe it?
Is there a more reasonable conclusion?
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Thought Question 2:
Theory: On average, men have lower
resting pulse rates than women do.
How could you go about trying to prove
or disprove that? Would it be sufficient
to measure the pulse rates of one member
of each sex? Two members of each sex?
What information about men’s and
women’s pulse rates would help you
decide how many people to measure?
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Thought Question 3:
Suppose you were to learn that the large
state university in a particular state
graduated more students who eventually
went on to become millionaires than any of
the small liberal arts colleges in the state.
Would that be a fair comparison?
How should the numbers be presented
in order to make it a fair comparison?
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Thought Question 4:
In its March 3–5, 1995 issue, USA Weekend
magazine asked readers to return a survey
with a variety of questions about sex and
violence on television. Of 65,142 readers
who responded, 97% were “very or
somewhat concerned about violence on TV”
(USA Weekend, 2–4 June 1995, p. 5).
Based on this survey, can you conclude that
about 97% of U.S. citizens are concerned
about violence on TV? Why or why not?
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1.1 Statistics
Statistics is a collection of
procedures and principles for
gaining and analyzing
information in order to help
people make decisions when
faced with uncertainty.
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Statistics in Your Own Life
Which route to go to school,
class, work?
Try each a few times
Then choose best one.
Sampling routes and comparing them
gained and analyzed useful
information to make a decision.
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Case Study 1.1:
Heart or
Hypothalamus?
Hypothalamus plays role in emotion, yet most
people think about the heart. Psychologist Lee
Salk studied role of heart in human relationships.
Observations:
• Rhesus monkey at zoo held baby on left,
by the heart, on 40 out of 42 occasions.
• Out of 287 human mothers (within 4 days
of giving birth), 237 or 83% held babies
on left – regardless of handedness.
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Case Study 1.1:
Heart or
Hypothalamus?
More Observations:
• Out of 438 shoppers leaving store with one
bag, exactly half carried bag on the left.
• Dental patients asked to hold a 5-inch ball
while teeth worked on. Substantially more
than half held it on the left (under stress).
Salk’s conjecture:
Must be survival value to having a newborn
placed close to sound of mother’s heartbeat.
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Case Study 1.1:
Heart or
Hypothalamus?
Controlled Experiment:
Baby nursery at NY City hospital.
• 1st group of newborns: Continuous sound
of human heartbeat over loudspeaker.
• 2nd group of newborns: no sound played.
Response: weight gain (or loss) after 4 days.
Results:
Infants treated to heartbeat sound gained
more weight (lost less) and cried less.
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1.2 Detecting Patterns
and Relationships
Obvious or Not?
• Average man taller than average woman.
• Taking aspirin helps prevent heart attacks.
• More likely to buy blue jeans in certain months
than others.
• Men have lower resting pulse rates than women.
• Listening to Mozart improves spatial reasoning.
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Statistical Studies
To conduct a statistical study
properly, one must
1. Get a representative sample.
2. Get a large enough sample.
3. Decide whether the study should
be an observational study or
a randomized experiment.
Example: Assess if men have lower
resting pulse rates than women.
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1. Get a representative sample.
Sample = those actually studied
Population = larger group from which
sample was chosen
Researchers want to extend results
beyond just the sample.
For pulse rates:
Convenient sample = members of your class.
Not valid, e.g., if entire track team in class.
Couldn’t extend to other age groups.
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2. Get a large enough sample.
How large is “large enough”?
Depends on how much the responses vary.
More variable within each group
larger sample needed to detect a difference.
For pulse rates:
• If all men had rate of 65 and all women had rate
of 75, then just need a few to see the difference.
• If men’s rate varied from 50 to 80 and women’s
rates ranged from 52 to 82, then would take
more measurements to see a difference.
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3. An observational Study
or Randomized Experiment?
Observational Study: merely observe things
about our sample.
Randomized Experiment: randomly assign
participants to one of various treatment
groups.
For pulse rates:
• Sufficient to measure or “observe” both pulse
rates and gender of people in sample.
• To learn if aspirin helps prevent heart attacks,
a randomized experiment would be better.
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Case Study 1.2: Does Aspirin Prevent
Heart Attacks?
Physicians’ Health Study (1988)
5-year randomized experiment
22,071 male physicians (40 to 84 years old).
• Group 1: took ordinary aspirin tablet
every other day.
• Group 2: took placebo (looked like aspirin
but no active ingredients).
Subjects did not know which group they
were assigned (called blinding).
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Case Study 1.2: Does Aspirin Prevent
Heart Attacks?
Condition
Aspirin
Placebo
Heart Attack
104
189
No Heart Attack
10,933
10,845
Attacks per 1000
9.42
17.13
Results:
• Heart attack rate in aspirin group only 55% of rate
in placebo group.
• Randomization other factors, such as amount of
exercise, expected to be similar for both groups.
• Subjects were male physicians. Results may not
extend to all males, nor to women.
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1.3 Don’t Be Deceived By
Improper Use of Statistics
Example 1
• Business Magazine sent 2000 questionnaires to
readers about Republican primary: Chrysler
president Lee Iacocca vs. VP George Bush.
• Based on only first 200 respondents, reported
Iacocca would beat Bush 54% to 47%.
• Sample not representative of population of all
people likely to vote: those who feel strongly
about an issue most likely to respond.
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Improper Use of Statistics
Example 2
• U.S. EPA study led to report that New Jersey
ranked 22nd in its release of toxic chemicals.
• Problem: wrong units … ranking was based
on total pounds released.
• Using appropriate rate of pounds released per
square mile, New Jersey ranked 4th on the list.
• Figures were misleading until adjusted for size.
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Improper Use of Statistics
Example 3
• Article headline:
“Study: Smoking May Lower Kids’ IQs”
• Headline implication: a causal connection.
• Problem: results based on an observational
study (since experiment would be unethical).
• Moral: Can’t make causal connections
from observational studies.
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Improper Use of Statistics
New study confirms too much pot impairs brain
“More evidence that chronic marijuana smoking impairs mental
ability: Researchers at the University of Iowa College of Medicine
say a test shows those who smoke seven or more marijuana joints
per week had lower math, verbal and memory scores than nonmarijuana users. Scores were particularly reduced when marijuana
users held a joint’s smoke in their lungs for longer periods.” San
Francisco Examiner, 13 March 1993, p. D-1.
Example 4
• Headline implication: a causal connection.
• Problem: based on an observational study
• Can conclude there is a relationship but
cannot conclude a causal connection.
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Case Study 1.3: A Mistaken Accusation
of Cheating
• Two students accused of cheating on multiple
choice medical exam due to whispering during one
part and wrong answers often matched each other.
• Licensing board estimated odds of having answers
as close as these two were < 1 in 10,000.
• At trial, statistician showed agreement in this exam
was no higher than in other exams.
• Key: two students were husband and wife, both
from India. Licensing board incorrectly assumed
they were just guessing. Instead, common mistakes
were often the right answers for India background.
• Whispering had to do with status of sick child.
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1.4 Summary and Conclusions
•There are both advantages and dangers of
using statistical methods.
•Results of a study are not enough!
•You need to know how data were collected,
who was asked, etc.
•Over the next several chapters, you will
become an educated consumer of statistical
information.
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